The Project “Math in a Cultural Context” (Yup’ik/Yupiaq, Alaska)
We situate the development of curriculum materials and a pedagogical approach within a long-term collaborative relationship with Yupiaq elders and expert Yupiaq teachers. Joint analyses of everyday activities revealed an underlying set of mathematical principles that guides those activities. The key concepts of qukaq (center), halving, symmetry, measuring, and verifying are the cultural and mathematical generative concepts. We also share our evolving understanding with examples of curriculum development at different stages of our work as well as an appreciation of our insider/outsider research group and how Yupiaq knowledge emerged from discussions, demonstrations, visual representation and translation, and how this knowledge continues to evolve and grow.

Yup’ik string figures
Several string games traditionally known among Yup’ik people (Yupiit) will be presented, with the view of shedding light on the mathematical ideas that have seemingly been involved in the creation of these procedural games. Epistemological and didactical issues raised by the potential use of string games as tools for teaching mathematics will then be discussed, both within a local perspective (cf. "culturally embedded mathematics") and at a larger level (string games as pedagogical support for teaching mathematics in various cultural contexts).

Sand drawing from Vanuatu
In Vanuatu (ex New-Hebrides), a cultural practice consists in drawing geometrical figures (mostly symmetric) in the sand (or in the ashes), tracing a continuous line with a finger, without lifting it from the ground and by ending the drawing at the starting point. The analysis of ethnographic datas leads us to make hypotheses about the mathematical concepts that underlie the creation and the practice of these geometrical drawings.
First, we will make some of these « sand drawings » of which a computer modeling (written in Python) will thereafter be presented. Then, we will discuss the sand-drawing educational perspectives. In particular, we will give evidence of some mathematical skills that this activity could bring into the classroom.

Deacon, A. B., & Wedgwood, C. H. (1934). Geometrical drawings from Malekula and other islands of the New Hebrides. Journal of the Royal Anthropological Institute of Great Britain and Ireland, 64, 129-175.

Weaving dualism in the AndesIn some areas of the Bolivian and Peruvian highlands, weaving processes in use since more than two millennia involve the use of logical and counting rules that shape textile designs and texture. Yet these logics grounded on symmetries and secondary on substitution are used in several domains of social organisation and life where they show a dualist, sometimes tripartite, way of thinking. We will break down the weaving process in order to make these logics understandable and connect them with the woven result (with two symmetrical faces), and then we will compare them with other more accessible expressions of Andean dualism. The learning method applied in a community of the Cuzco valley shows the important role of symmetries in the construction of knowledge. I have not found yet any pedagogical experience using these ways of knowing. Still looking for them.